MathDB

Problem 2

Part of 2013 Macedonian Team Selection Test

Problems(1)

Sums and products of digits and irrational numbers

Source: Macedonian TST for IMO 2013 - P2 day 1

3/28/2021
a) Denote by S(n)S(n) the sum of digits of a positive integer nn. After the decimal point, we write one after the other the numbers S(1),S(2),...S(1),S(2),.... Show that the number obtained is irrational.
b) Denote by P(n)P(n) the product of digits of a positive integer nn. After the decimal point, we write one after the other the numbers P(1),P(2),...P(1),P(2),.... Show that the number obtained is irrational.
number theoryirrational number